I have recently build a platform above my house at y=250. As my house is at ground level, I would prefer not to have to build a tower every time I wish to get up there, and ideally I would like to not have a tower visible between the platform and my house.
With this in mind, I decided that nether portals would be the way to go. I have a nether portal in my house at y=57 and one on my platform at y=250, I also have portals in the same places at y=70 and y=115 in the nether.
Unfortunately, the portal at y=155 in the nether sends me back to the portal in my house. I understand that this is because the house portal is closer. Is there any possible way for me to travel to my platform using nether portals? Or failing that, any way to travel there without building something between my house and the platform?
Not only is this unfortunately impossible with your current setup, it’s impossible to reach a high overworld portal from the Nether as of 1.2.4:
As of the 1.2 update, there is a confirmed bug in which the “portal search” performed during travel back from the nether will not find any overworld portal above a height of 128. Thus, it is not possible to travel back to the overworld and land at a portal which is above y = 128.
From the Minecraft Wiki article.
Additionally, without mods, there is currently no way to move upwards without some sort of connecting structure, save perhaps a vertical TNT cannon, and it seems to me that you want something a bit more usable than that.
Now, in theory, once this bug is fixed, you could build a transport bridge a few blocks out in the Nether and the same number of block multiplied by 8 in the overworld coordinated just so that the higher platform is closer to the new portal, but it would be complex to do.
Until then, you’re stuck with regular transportation.